%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP166-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:30 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 8 RR)
% Number of literals : 25 ( 24 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
greatest_lower_bound(a,multiply(b,a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat3b) ).
cnf(c2,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(X2,multiply(X3,X2)) = greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c6,plain,
multiply(greatest_lower_bound(identity,X2),X3) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(identity,X2),X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c9,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(greatest_lower_bound(identity,X2),X3) = multiply(greatest_lower_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c7,c10]) ).
cnf(c12,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c4,c11]) ).
cnf(c13,plain,
greatest_lower_bound(X2,multiply(b,X2)) = multiply(greatest_lower_bound(b,identity),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(substitution,[status(thm)],[c8]) ).
cnf(c15,plain,
multiply(greatest_lower_bound(b,identity),X2) = multiply(greatest_lower_bound(identity,b),X2),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(substitution,[status(thm)],[c8]) ).
cnf(c17,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,axiom,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
greatest_lower_bound(identity,b) = identity,
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
multiply(greatest_lower_bound(identity,b),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(greatest_lower_bound(identity,b),X2) = X2,
inference(transitivity,[status(thm)],[c20,c2]) ).
cnf(c22,plain,
multiply(greatest_lower_bound(b,identity),X2) = X2,
inference(transitivity,[status(thm)],[c15,c21]) ).
cnf(c23,plain,
greatest_lower_bound(X2,multiply(b,X2)) = X2,
inference(transitivity,[status(thm)],[c13,c22]) ).
cnf(c24,plain,
greatest_lower_bound(a,multiply(b,a)) = a,
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
$false,
inference(resolution,[status(thm)],[c1,c24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP166-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:38:00 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.45 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.09/0.45
% 0.09/0.45 % SZS status Unsatisfiable
% 0.09/0.45
% 0.09/0.45 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45
% 0.09/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------